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This paper aims to examine the influence of radiative nanoparticles on incompressible electrically conducting upper convected Maxwell fluid (rate type fluid) flow over a convectively heated exponential stretching sheet with suction/injection in the presence of heat source taking chemical reaction into account. Also, a comparison of the flow behavior of Newtonian and Maxwell fluid containing nanoparticles under the effect of different thermophysical parameters is elaborated. Velocity, temperature and nanoparticle volume fractions are assumed to have exponential distribution at boundary. Buongiorno model is considered for nanofluid transport.

The equations, which govern the flow, are reduced to ordinary differential equations using suitable transformation. The transformed equations are solved using a robust homotopy analysis method. The convergence of the homotopy series solution is explicitly discussed. The present results are compared with the results reported in the literature and are found to be in good agreement.

It is observed from the present study that larger relaxation time leads to slower recovery, which results in a decrease in velocity, whereas temperature and nanoparticle volume fraction is increased. Maxwell nanofluid has lower velocity with higher temperature and nanoparticle volume fraction when compared with Newtonian counterpart. Also, the presence of magnetic field leads to decrease the velocity of the nanofluid and enhances the skin coefficient friction. The existence of thermal radiation and heat source enhance the temperature. Further, the presence of chemical reaction leads to decrease in nanoparticle volume fraction. Higher value of Deborah number results in lower the rate of heat and mass transfer.

The novelty of present work lies in understanding the impact of fluid elasticity and radiative nanoparticles on the flow over convectively heated exponentially boundary surface in the presence of a magnetic field using homotopy analysis method. The current results may help in designing electronic and industrial applicants. The present outputs have not been considered elsewhere.

This study presents a mathematical approach and model that can be useful to investigate the thermal performance of fluids with microstructures via hybrid nanoparticles in conventional fluid. It has been found from the extensive literature survey that no study has been conducted to investigate buoyancy effects on the flow of Maxwell fluid comprised of hybrid microstructures and heat generation aspects through the non-Fourier heat flux model.

Non-Fourier heat flux model and non-Newtonian stress–strain rheology with momentum and thermal relaxation phenomena are used to model the transport of heat and momentum in viscoelastic fluid over convectively heated surface. The role of suspension of mono and hybrid nanostructures on an increase in the thermal efficiency of fluid is being used as a medium for transportation of heat energy. The governing mathematical problems with thermo-physical correlations are solved via shooting method.

It is noted from the simulations that rate of heat transfer is much faster in hybrid nanofluid as compare to simple nanofluid with the increasing heat-generation coefficient. Additionally, an increment in the thermal relaxation time leads to decrement in the reduced skin friction coefficient; however, strong behavior of Nusselt number is shown when thermal relaxation time becomes larger for hybrid nanofluid as well as simple nanofluid.

According to the literature survey, no investigation has been made on buoyancy effects of Maxwell fluid flow with hybrid microstructures and heat generation aspects through non-Fourier heat flux model. The authors confirm that this work is original, and it has neither been published elsewhere nor is it currently under consideration for publication elsewhere.

In this study, the stationary flow of a polymeric fluid governed by the upper convected Maxwell law is computed in a 2‐D convergent geometry. A finite element method is used to obtain non‐linear discretized equations, solved by an iterative Picard (fixed point) algorithm. At each step, two sub‐systems are successively solved. The first one represents a Newtonian fluid flow (Stokes equations) perturbed by known pseudo‐body forces expressing fluid elasticity. It is solved by minimization of a functional of the velocity field, while the pressure is eliminated by penalization. The second sub‐system reduces to the tensorial differential evolution equation of the extra‐stress tensor for a given velocity field. It is solved by the so‐called ‘non‐consistent Petrov‐Galerkin streamline upwind’ method. As with other decoupled techniques applied to this problem, our simulation fails for relatively low values of the Weissenberg viscoelastic number. The value of the numerical limit point depends on the mesh refinement. When convergence is reached, the numerical solutions for velocity, pressure and stress fields are similar to those obtained by other authors with very costly mixed methods.

This paper aims to describe the laminar flow of Maxwell fluid past a non-isothermal rigid plate with a stream wise pressure gradient. Heat transfer mechanism is analyzed in the context of non-Fourier heat conduction featuring thermal relaxation effects.

Flow field is permeated to uniform transverse magnetic field. The governing transport equations are changed to globally similar ordinary differential equations, which are tackled analytically by homotopy analysis technique. Homotopy analysis method-Padè approach is used to accelerate the convergence of homotopy solutions. Also, numerical approximations are made by means of shooting method coupled with fifth-order Runge-Kutta method.

The solutions predict that fluid relaxation time has a tendency to suppress the hydrodynamic boundary layer. Also, heat penetration depth reduces for increasing values of thermal relaxation time. The general trend of wall temperature gradient appears to be similar in Fourier and Cattaneo–Christov models.

An important implication of current research is that the thermal relaxation time considerably alters the temperature and surface heat flux.

Current problem even in case of Newtonian fluid has not been attempted previously.

The purpose of this paper is to investigate the two-dimensional flow of Maxwell fluid with power law heat flux and heat source over a stretched surface.

The governing partial differential equations are reduced into ordinary differential equations by applying similarity transformations. Series solutions of velocity and temperature are found by adopting homotopy analysis method (HAM).

It is found that the velocity decreases by increasing Deborah number and suction parameter. It is also observed that the heat generation parameter leads to a decrease in temperature. Furthermore, the numerical values of local Nusselt number decreased with an increase in Deborah number.

A useful source of information for the investigators on the field of non-Newtonian fluids with heat transfer.

This paper discusses the boundary layer flow of Maxwell fluid with power law heat flux in the presence of heat source.

The purpose of the paper was the application of computational fluid dynamics (CFD) techniques in fluid flow using Maxwell’s equation for partial slip modelling, estimating the flow parameters, and selecting tangential momentum accommodation coefficient (TMAC) for tight rock samples in permeability calculations.

The paper presents a numerical analysis of fluid flow in a low-porosity rock sample by using CFD. Modelling results allowed to determine mass flow rates in a rock sample and to calculate permeability values using a modified Darcy’s equation. Three-dimensional (3D) geometrical model of rock sample generated using computed X-ray tomography was used in the analysis. Steady-state calculations were carried out for defined boundary conditions in the form of pressure drop. The simulations were applied taking into account the slip phenomenon described by Maxwell’s slip model and TMAC.

Values of permeability were calculated for different values of TMAC, which vary from 0 to 1. Results in the form of gas mass flow rates were compared with the measured value of permeability for rock sample, which confirmed the high accuracy of the presented model.

Calculations of fluid flow in porous media using CFD can be used to determine rock samples’ permeability. In slip flow regime, Maxwell’s slip model can be applied and the empirical value of TMAC can be properly estimated.

This paper presents the usage of CFD, Maxwell’s equation for partial slip modelling, in fluid flow mechanism for tight rock samples. 3D geometric models were generated using created pre-processor (poROSE software) and applied in the raw form for simulation.

The purpose of this paper is to undertake an unsteady flow problem of an anomalous Maxwell fluid. The flow takes place between two side walls over a plate perpendicular to them and is driven by a sudden pressure force with constant gradient.

A finite element method is invoked and is blended with a finite difference method for left Caputo fractional time derivatives in order to study the anomalous dynamics of the fluid.

A numerical scheme for the constitutive equations of the prescribed flow in order to approximate the velocity field is designed. The graphical results to draw different physical conclusions on the flow problem are also presented.

A rigorous mathematical exposition of the numerical scheme is provided and the results are valid for large values of the parameters.

The purpose of this paper is to address the heat and mass transfer effects in three-dimensional flow of Maxwell fluid over a stretching surface with convective boundary conditions. Mass transfer is considered in the presence of first order chemical reaction. Conservation laws of energy and concentration are based upon the Soret and Dufour effects. Convergent series solutions to the resulting non-linear problems are developed. Effects of Biot and Deborah numbers on the Sherwood number are decreasing. Local Nusselt reduces with an increase in Eckert numbers. It is also interesting to note further that variations of Prandtl and Biot numbers on the Nusselt number are increasing while Sherwood number decreases with an increase in Prandtl number.

The involved partial differential systems are reduced to the ordinary differential systems using appropriate transformations. Series solutions by homotopy analysis method are constructed and analyzed. Graphical results are presented and examined in detail.

It is found that roles of Deborah and Biot parameters on the Nusselt number are opposite. However, the Sherwood number is qualitative similar for both Biot and Deborah numbers. It is also interesting to note further that variations of Prandtl and Biot numbers on the Nusselt and Sherwood numbers are similar.

The purpose of present communication is to investigate the three-dimensional flow of Maxwell fluid over a stretching surface with convective condition. Analysis has been carried out in the presence of mass transfer with first order chemical reaction and Soret and Dufour effects.

This study aims to investigate the two-dimensional magnetohydrodynamic flow and heat transfer of a fractional Maxwell nanofluid between inclined cylinders with variable thickness. Considering the cylindrical coordinate system, the constitutive relation of the fractional viscoelastic fluid and the fractional dual-phase-lag (DPL) heat conduction model, the boundary layer governing equations are first formulated and derived.

The newly developed finite difference scheme combined with the L1 algorithm is used to numerically solve nonlinear fractional differential equations. Furthermore, the effectiveness of the algorithm is verified by a numerical example.

Based on numerical analysis, the effects of parameters on velocity and temperature are revealed. Specifically, the velocity decreases with the increase of the fractional derivative parameter α owing to memory characteristics. The temperature increase with the increase of fractional derivative parameter ß due to a decrease in thermal resistance. From a physical perspective, the phase lag of the heat flux vector and temperature gradients τ_q and τ_T exhibit opposite trends to the temperature. The ratio τ_T/τ_q plays an important role in controlling different heat conduction behaviors. Increasing the inclination angle θ, the types and volume fractions of nanoparticles Φ can increase velocity and temperature, respectively.

Fractional Maxwell nanofluid flows from a fixed-thickness pipe to an inclined variable-thickness pipe, and the fractional DPL heat conduction model based on materials is considered, which provides a basis for the safe and efficient transportation of high-viscosity and condensable fluids in industrial production.

The purpose of this paper is to investigate the three-dimensional flow of Maxwell fluid with variable thermal conductivity in presence of heat source/sink.

Similarity transformations are utilized to reduce the nonlinear partial differential equations into ordinary differential equations. The governing nonlinear problems are solved by homotopy analysis method.

The paper found that the velocities decrease while temperature increases for higher Hartman number. It is also seen that the thermal boundary layer thickness and temperature are increased with an increase in variable thermal conductivity parameter and heat source/sink parameter.

Heat transfer analysis with heat source/sink has pivotal role in many industrial applications like cooling of an infinite metallic plate in a cooling bath, drawing of plastic films, nuclear plants, gas turbines, various propulsion devices for missiles, space vehicles and processes occurring at high temperatures.

This study discusses the magnetohydrodynamic three-dimensional flow of Maxwell fluid with variable thermal conductivity and heat source/sink. No such analysis exists in the literature yet.